Question

Jaime has $2. 60 in dimes and nickels. The number of dimes is 14 more than the number of nickels. How many of each coin does he have?.

Answer 1

Dime is one-tenth of a dollar, while nickle is one-twentieth part of a dollar. Jaime has got 22 dimes and 4 nickle coin in this case.

How to form mathematical expression from the given description?

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the given case, since number of dimes is given in terms of number of nickels, so lets assume that:

• Number of nickle Jaime got = $x$

• Number of dime Jaime got = 14 more than the number of nickle = $14 +x$

Since 1 nickle's cost = $0.05,

thus, x nickles' cost = $x \times 0.05$ (in dollars)

And as 1 dime's cost = $0.10,

thus, 14 + x dimes' cost = $0.10 \times (14 + x)$ (in dollars)

Total amount Jamie have = Amount by nickles + Amount by dimes

Total amount Jamie have = $0.10(14+x) + 0.05x$  (in dollars) = $2.60 (as given in the problem)

Thus, we get:

$0.10 (14+x) + 0.05x = 2.60\\1.4 + 0.10x + 0.05x = 2.60\\\\\text{Subtracting 1.4 from both the sides}\\\\0.15x = 1.2\\\text{Dividing both the sides by 0.15}\\\\\dfrac{0.15x}{0.15} = \dfrac{1.2}{0.15}\\\\x = 8$

Thus, Jamie got  x = 8 nickles.

And number of dimes he got = x + 14 = 8 + 14 = 22

Thus,  Jaime has got 22 dimes and 4 nickle coin in this case.

Learn more about forming equations here:

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